S\'eparation de sources doublement non stationnaire

Adrien Meynard (I2M)

arxiv: 1906.09950 · v1 · pith:77OJT37Nnew · submitted 2019-06-24 · 📡 eess.SP

S\'eparation de sources doublement non stationnaire

Adrien Meynard (I2M) This is my paper

Pith reviewed 2026-05-25 17:24 UTC · model grok-4.3

classification 📡 eess.SP

keywords blind source separationnonstationary signalswavelet transformdeformed stationary signalsjoint estimationtime-dependent mixingdoubly nonstationary

0 comments

The pith

An algorithm jointly estimates sources, time-varying mixing matrix, deformations and spectra for doubly nonstationary blind source separation using wavelet approximations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper addresses blind source separation where both the mixing matrix is time-dependent and the sources are nonstationary deformed stationary signals. It introduces an algorithm that performs joint estimation by exploiting approximations of the wavelet transform of these signals. A sympathetic reader would care because this extends BSS to more realistic scenarios with changing conditions and nonstationary sources, such as in signal processing applications. The method is evaluated on numerical simulations against other nonstationary BSS algorithms.

Core claim

The central claim is that suitable approximations for the behavior of the wavelet transform of deformed stationary signals enable an algorithm for joint BSS and estimation of stationarity-breaking deformations and spectra in the doubly nonstationary case.

What carries the argument

Approximations of the wavelet transform for nonstationary deformed stationary signals, which support the joint estimation procedure.

If this is right

The algorithm can separate sources under time-dependent mixing.
It estimates the deformations that make the sources nonstationary.
It also estimates the spectra of the original stationary signals.
Performance is demonstrated on numerical simulations and compares favorably to other nonstationary BSS methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Such methods could be applied to real-world data like audio recordings with varying environments.
Extensions might involve adapting the approximations for different types of deformations.
Connections to time-frequency analysis in other signal processing tasks could be explored.

Load-bearing premise

The wavelet transform approximations for the behavior of deformed stationary signals remain accurate enough for the joint estimation to succeed.

What would settle it

Simulations or experiments where the wavelet approximations are intentionally violated would result in poor separation performance or inaccurate estimates of deformations and spectra.

read the original abstract

Blind source separation (BSS) techniques aims at joint estimation of source signals and a mixing matrix from observations of mixtures. This paper addresses a doubly nonstationary BSS problem, where the mixing matrix is time dependent and sources are nonstationary, more precisely deformed stationary signals, following the model of [1]. An algorithm for joint BSS and estimation of stationarity-breaking deformations and spectra is introduced, that exploits suitable approximations for the behavior of the wavelet transform of such nonstationary signals. The performance of the approach is evaluated on numerical simulations, and compared with other nonstationary BSS algorithms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a new joint BSS algorithm for the doubly nonstationary case via wavelet approximations on the model from [1], but the abstract reports no numbers, no error analysis, and no validity regime for those approximations.

read the letter

The main takeaway is that this work extends an existing model to handle time-varying mixing together with deformed nonstationary sources by adding a wavelet approximation step for the joint estimation of mixing, deformations, and spectra. That combination is new relative to the cited reference [1]. The algorithmic construction itself looks like a straightforward extension rather than anything circular or self-referential. The paper does a reasonable job of framing the problem and naming the tool (wavelet approximations) that lets the joint estimator proceed. For readers already working on nonstationary BSS, the idea of folding the deformation estimation into the same procedure could be useful as a starting point. The soft spots are exactly where the stress-test note points. The abstract claims numerical simulations and comparisons with other algorithms, yet supplies none of the actual results, error metrics, or even basic tables. More critically, there is no derivation, bound, or operating range stated for the wavelet approximations that the whole method rests on. Without that, it is impossible to tell whether the approach works only in narrow regimes or more generally. The full manuscript might contain those details, but nothing in the provided abstract or stress-test indicates they are present. This is a specialized signal-processing paper aimed at people already deep in blind source separation. A reader in that niche could extract the algorithmic idea and try to fill in the missing analysis themselves. It is not broad enough or evidenced enough for a general audience. I would still send it to peer review so that referees can check whether the full text supplies the missing bounds and quantitative results; the core idea is clear enough to be worth that step.

Referee Report

2 major / 2 minor

Summary. The paper introduces an algorithm for joint blind source separation (BSS) and estimation of a time-dependent mixing matrix, stationarity-breaking deformations, and source spectra in a doubly nonstationary setting. Sources follow the deformed stationary model of [1]; the method exploits approximations to the wavelet transform of such signals for the joint estimation task and reports performance via numerical simulations compared against other nonstationary BSS algorithms.

Significance. If the wavelet approximations remain sufficiently accurate, the approach would provide a unified framework for a difficult class of BSS problems that standard methods handle separately. The explicit comparison to existing algorithms and the use of numerical simulations are strengths that would support incremental progress in the field.

major comments (2)

[Abstract] Abstract: the claim that 'performance of the approach is evaluated on numerical simulations' is unsupported by any quantitative results, error metrics, or validation details; the central claim therefore rests on unshown evidence.
[Abstract (method description)] The algorithm rests on 'suitable approximations for the behavior of the wavelet transform of such nonstationary signals'; no derivation, error bound, or parameter range is supplied under which these approximations remain accurate enough for the joint estimation of mixing, deformations, and spectra to succeed. This assumption is load-bearing for the method's validity.

minor comments (2)

[Title] The title contains a typographical error ('Sépération' instead of 'Séparation').
[Abstract] The abstract does not specify the number of sources, the form of the time-dependent mixing, or the deformation model parameters used in the simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and constructive feedback on our manuscript. We address each major comment below and will revise the manuscript to improve clarity and rigor where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that 'performance of the approach is evaluated on numerical simulations' is unsupported by any quantitative results, error metrics, or validation details; the central claim therefore rests on unshown evidence.

Authors: The abstract is intended as a concise summary; the full manuscript contains a dedicated simulation section with quantitative comparisons (error metrics, performance tables, and validation against other nonstationary BSS methods). To address the concern directly, we will revise the abstract to include one or two key quantitative results and a brief description of the simulation setup. revision: yes
Referee: [Abstract (method description)] The algorithm rests on 'suitable approximations for the behavior of the wavelet transform of such nonstationary signals'; no derivation, error bound, or parameter range is supplied under which these approximations remain accurate enough for the joint estimation of mixing, deformations, and spectra to succeed. This assumption is load-bearing for the method's validity.

Authors: The approximations are introduced in the method section and are motivated by the deformed-stationary model of reference [1]; their practical accuracy is supported by the reported simulation results. We agree that an explicit derivation, error analysis, and validity range would strengthen the paper. We will add a new subsection providing the derivation of the wavelet approximations, first-order error bounds, and the parameter regimes (e.g., deformation speed, wavelet scale) under which the joint estimation remains reliable. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to prior model; algorithm remains independent construction

full rationale

The paper presents an algorithmic construction for joint BSS, deformation, and spectrum estimation that exploits wavelet approximations drawn from the model of [1]. No derivation step, equation, or result is shown to reduce by construction to fitted inputs, self-referential definitions, or a load-bearing self-citation chain; the central claim is an independent algorithmic procedure whose performance is assessed via separate numerical simulations. The single reference to [1] constitutes at most a minor self-citation that does not force the reported outcomes.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be extracted. The central claim rests on unstated validity of wavelet approximations for deformed signals.

pith-pipeline@v0.9.0 · 5616 in / 904 out tokens · 18315 ms · 2026-05-25T17:24:25.413365+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

[1]

Ces hypothèses sont appropriées pour décrire de nombreux si - gnaux de la vie réelle

https://github.com/AdMeynard/JEFAS 2 Modèle 2.1 Une classe de signaux non stationnaires Dans ce qui suit, nous considérons les signaux non station- naires comme des versions déformées de signaux stationnair es. Ces hypothèses sont appropriées pour décrire de nombreux si - gnaux de la vie réelle. En effet, différentes classes d’opér ateurs qui brisent la s...

work page
[2]

M EYNARD et B

A. M EYNARD et B. T ORRÉSANI , « Spectral Analysis for Nonstationary Audio », IEEE/ACM Transactions on Au- dio, Speech and Language Processing , vol. 26, p. 2371 – 2380, déc. 2018

work page 2018
[3]

C OMON et C

P . C OMON et C. J UTTEN , Handbook of Blind Source Se- paration, Independent Component Analysis and Applica- tions. Academic Press (Elsevier), fév. 2010

work page 2010
[4]

B ELOUCHRANI , K

A. B ELOUCHRANI , K. A BED -M ERAIM , J.-F. C ARDOSO et E. M OULINES , « A blind source separation technique using second-order statistics », IEEE Transactions on Si- gnal Processing, vol. 45, p. 434–444, fév. 1997

work page 1997
[5]

T HIRION -M OREAU et M

N. T HIRION -M OREAU et M. A MIN , « Chapter 11 - qua- dratic time-frequency domain methods », in Handbook of Blind Source Separation (P . COMON et C. J UTTEN , éds), p. 421 – 466, Oxford : Academic Press, 2010

work page 2010
[6]

B ELOUCHRANI , M

A. B ELOUCHRANI , M. A MIN , N. T HIRION -M OREAU et Y . D. ZHANG , « Source separation and localization using time-frequency distributions : An overview », IEEE Si- gnal Processing Magazine, vol. 30, p. 97–107, nov. 2013

work page 2013
[7]

P HAM et J.-F

D.-T. P HAM et J.-F. C ARDOSO , « Blind separation of instantaneous mixtures of nonstationary sources », IEEE Transactions on Signal Processing , vol. 49, p. 1837– 1848, sept. 2001

work page 2001
[8]

K AFTORY et Y

R. K AFTORY et Y . Y . Z EEVI , « Blind separation of time/position varying mixtures », IEEE Transactions on Image Processing, vol. 22, p. 104–118, jan. 2013

work page 2013
[9]

R. E. P RIETO et P . JINACHITRA , « Blind source separa- tion for time-variant mixing systems using piecewise li- near approximations », in Proceedings. IEEE Internatio- nal Conference on Acoustics, Speech, and Signal Proces- sing, 2005., vol. 5, p. v/301–v/304, mars 2005

work page 2005
[10]

C LERC et S

M. C LERC et S. M ALLAT , « Estimating deformations of stationary processes », Ann. Statist. , vol. 31, p. 1772– 1821, 12 2003

work page 2003
[11]

O MER et B

H. O MER et B. T ORRÉSANI , « Time-frequency and time- scale analysis of deformed stationary processes, with ap- plication to non-stationary sound modeling », Applied and Computational Harmonic Analysis , vol. 43, no. 1, p. 1 – 22, 2017

work page 2017
[12]

S TOWELL , Computational Analysis of Sound Scenes and Events, chap

D. S TOWELL , Computational Analysis of Sound Scenes and Events, chap. Computational Bioacoustic Scene Ana- lysis, p. 303–333. Springer, 2018

work page 2018
[13]

V INCENT , R

E. V INCENT , R. G RIBONVAL et C. F ÉVOTTE , « Perfor- mance measurement in blind audio source separation », IEEE Transactions on Audio, Speech, and Language Pro- cessing, vol. 14, p. 1462–1469, juil. 2006

work page 2006
[14]

M OREAU et O

E. M OREAU et O. M ACCHI , « A one stage self-adaptive algorithm for source separation », in Proceedings of ICASSP ’94. IEEE International Conference on Acous- tics, Speech and Signal Processing , vol. iii, p. III/49– III/52, avril 1994

work page 1994

[1] [1]

Ces hypothèses sont appropriées pour décrire de nombreux si - gnaux de la vie réelle

https://github.com/AdMeynard/JEFAS 2 Modèle 2.1 Une classe de signaux non stationnaires Dans ce qui suit, nous considérons les signaux non station- naires comme des versions déformées de signaux stationnair es. Ces hypothèses sont appropriées pour décrire de nombreux si - gnaux de la vie réelle. En effet, différentes classes d’opér ateurs qui brisent la s...

work page

[2] [2]

M EYNARD et B

A. M EYNARD et B. T ORRÉSANI , « Spectral Analysis for Nonstationary Audio », IEEE/ACM Transactions on Au- dio, Speech and Language Processing , vol. 26, p. 2371 – 2380, déc. 2018

work page 2018

[3] [3]

C OMON et C

P . C OMON et C. J UTTEN , Handbook of Blind Source Se- paration, Independent Component Analysis and Applica- tions. Academic Press (Elsevier), fév. 2010

work page 2010

[4] [4]

B ELOUCHRANI , K

A. B ELOUCHRANI , K. A BED -M ERAIM , J.-F. C ARDOSO et E. M OULINES , « A blind source separation technique using second-order statistics », IEEE Transactions on Si- gnal Processing, vol. 45, p. 434–444, fév. 1997

work page 1997

[5] [5]

T HIRION -M OREAU et M

N. T HIRION -M OREAU et M. A MIN , « Chapter 11 - qua- dratic time-frequency domain methods », in Handbook of Blind Source Separation (P . COMON et C. J UTTEN , éds), p. 421 – 466, Oxford : Academic Press, 2010

work page 2010

[6] [6]

B ELOUCHRANI , M

A. B ELOUCHRANI , M. A MIN , N. T HIRION -M OREAU et Y . D. ZHANG , « Source separation and localization using time-frequency distributions : An overview », IEEE Si- gnal Processing Magazine, vol. 30, p. 97–107, nov. 2013

work page 2013

[7] [7]

P HAM et J.-F

D.-T. P HAM et J.-F. C ARDOSO , « Blind separation of instantaneous mixtures of nonstationary sources », IEEE Transactions on Signal Processing , vol. 49, p. 1837– 1848, sept. 2001

work page 2001

[8] [8]

K AFTORY et Y

R. K AFTORY et Y . Y . Z EEVI , « Blind separation of time/position varying mixtures », IEEE Transactions on Image Processing, vol. 22, p. 104–118, jan. 2013

work page 2013

[9] [9]

R. E. P RIETO et P . JINACHITRA , « Blind source separa- tion for time-variant mixing systems using piecewise li- near approximations », in Proceedings. IEEE Internatio- nal Conference on Acoustics, Speech, and Signal Proces- sing, 2005., vol. 5, p. v/301–v/304, mars 2005

work page 2005

[10] [10]

C LERC et S

M. C LERC et S. M ALLAT , « Estimating deformations of stationary processes », Ann. Statist. , vol. 31, p. 1772– 1821, 12 2003

work page 2003

[11] [11]

O MER et B

H. O MER et B. T ORRÉSANI , « Time-frequency and time- scale analysis of deformed stationary processes, with ap- plication to non-stationary sound modeling », Applied and Computational Harmonic Analysis , vol. 43, no. 1, p. 1 – 22, 2017

work page 2017

[12] [12]

S TOWELL , Computational Analysis of Sound Scenes and Events, chap

D. S TOWELL , Computational Analysis of Sound Scenes and Events, chap. Computational Bioacoustic Scene Ana- lysis, p. 303–333. Springer, 2018

work page 2018

[13] [13]

V INCENT , R

E. V INCENT , R. G RIBONVAL et C. F ÉVOTTE , « Perfor- mance measurement in blind audio source separation », IEEE Transactions on Audio, Speech, and Language Pro- cessing, vol. 14, p. 1462–1469, juil. 2006

work page 2006

[14] [14]

M OREAU et O

E. M OREAU et O. M ACCHI , « A one stage self-adaptive algorithm for source separation », in Proceedings of ICASSP ’94. IEEE International Conference on Acous- tics, Speech and Signal Processing , vol. iii, p. III/49– III/52, avril 1994

work page 1994